Magnetic Resonance Imaging (MRI) is a widespread medical imaging technology. Some MRI applications (e.g., time resolved magnetic resonance angiography, cardiac imaging, dynamic contrast enhanced tumor imaging) seek to acquire a series of magnetic resonance (MR) images as quickly as possible. Some of these dynamic imaging applications use radial projections in either two-dimensional (2D) or three-dimensional (3D) spaces to acquire k-space data. Radial projections pass through and acquire the center of k-space where more object energy is located. Using radial projections may speed up acquisition times enough to remove the need to do cardiac or respiratory gating and may also reduce and/or eliminate bolus timing considerations in contrast enhanced imaging. In some examples, radial 3D acquisitions facilitate under-sampling a data space while still producing acceptable image quality.
Conventional systems have attempted to evenly distribute subsets of the full number of projections over the k-space volume. These conventional attempts have recognized that the order in which 3D radial projections are acquired affects image quality. Thus, conventional approaches have attempted to evenly distribute 3D projections in the volume being imaged. One conventional approach to distributing 3D projections is the 3D golden means algorithm of Chan et al., MRM 2009; 61(2): p 354. The 3D golden means algorithm attempts to order projections with nearly equidistant spacing regardless of time scale. While the 3D golden means algorithm improves over a purely random approach for some projection types, it may be limited to acquiring only a single radial projection per repetition time (TR). While the 3D golden means algorithm is useful for single radial projections, it may not be useful for bent trajectories or for multi-echo trajectories. Additionally, other conventional approaches may also be unsuitable for bent and/or multi-echo trajectories.
Conventional approaches that plan multi-echo trajectories may produce trajectories that lead to bunching of signals. This bunching may lead to different image quality at different points in k-space. For example, some regions may be sampled adequately and/or experience an acceptable number and/or type of artifacts while other regions may not be sampled adequately and/or may experience an unacceptable number and/or type of artifacts.